scholarly journals Convergence and Numerical Solution of a Model for Tumor Growth

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1355
Author(s):  
Juan J. Benito ◽  
Ángel García ◽  
María Lucía Gavete ◽  
Mihaela Negreanu ◽  
Francisco Ureña ◽  
...  

In this paper, we show the application of the meshless numerical method called “Generalized Finite Diference Method” (GFDM) for solving a model for tumor growth with nutrient density, extracellular matrix and matrix degrading enzymes, [recently proposed by Li and Hu]. We derive the discretization of the parabolic–hyperbolic–parabolic–elliptic system by means of the explicit formulae of the GFDM. We provide a theoretical proof of the convergence of the spatial–temporal scheme to the continuous solution and we show several examples over regular and irregular distribution of points. This shows the feasibility of the method for solving this nonlinear model appearing in Biology and Medicine in complicated and realistic domains.

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0245708
Author(s):  
Eun Seob Lim ◽  
Seung-Youb Baek ◽  
Taeyoung Oh ◽  
Minseon Koo ◽  
Joo Young Lee ◽  
...  

Bacillus cereus is a foodborne pathogen and can form biofilms on food contact surfaces, which causes food hygiene problems. While it is necessary to understand strain-dependent variation to effectively control these biofilms, strain-to-strain variation in the structure of B. cereus biofilms is poorly understood. In this study, B. cereus strains from tatsoi (BC4, BC10, and BC72) and the ATCC 10987 reference strain were incubated at 30°C to form biofilms in the presence of the extracellular matrix-degrading enzymes DNase I, proteinase K, dispase II, cellulase, amyloglucosidase, and α-amylase to assess the susceptibility to these enzymes. The four strains exhibited four different patterns in terms of biofilm susceptibility to the enzymes as well as morphology of surface-attached biofilms or suspended cell aggregates. DNase I inhibited the biofilm formation of strains ATCC 10987 and BC4 but not of strains BC10 and BC72. This result suggests that some strains may not have extracellular DNA, or their extracellular DNA may be protected in their biofilms. In addition, the strains exhibited different patterns of susceptibility to protein- and carbohydrate-degrading enzymes. While other strains were resistant, strains ATCC 10987 and BC4 were susceptible to cellulase, suggesting that cellulose or its similar polysaccharides may exist and play an essential role in their biofilm formation. Our compositional and imaging analyses of strains ATCC 10987 and BC4 suggested that the physicochemical properties of their biofilms are distinct, as calculated by the carbohydrate to protein ratio. Taken together, our study suggests that the extracellular matrix of B. cereus biofilms may be highly diverse and provides insight into the diverse mechanisms of biofilm formation among B. cereus strains.


2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Yong-Hong Fan ◽  
Lin-Lin Wang

We propose a new algorithm for solving the terminal value problems on a q-difference equations. Through some transformations, the terminal value problems which contain the first- and second-order delta-derivatives have been changed into the corresponding initial value problems; then with the help of the methods developed by Liu and H. Jafari, the numerical solution has been obtained and the error estimate has also been considered for the terminal value problems. Some examples are given to illustrate the accuracy of the numerical methods we proposed. By comparing the exact solution with the numerical solution, we find that the convergence speed of this numerical method is very fast.


2012 ◽  
Vol 263-266 ◽  
pp. 1315-1318
Author(s):  
Kun Ming Yu ◽  
Ming Gong Lee

This paper is to discuss how Python can be used in designing a cluster parallel computation environment in numerical solution of some block predictor-corrector method for ordinary differential equations. In the parallel process, MPI-2(message passing interface) is used as a standard of MPICH2 to communicate between CPUs. The operation of data receiving and sending are operated and controlled by mpi4py which is based on Python. Implementation of a block predictor-corrector numerical method with one and two CPUs respectively is used to test the performance of some initial value problem. Minor speed up is obtained due to small size problems and few CPUs used in the scheme, though the establishment of this scheme by Python is valuable due to very few research has been carried in this kind of parallel structure under Python.


Molecules ◽  
2020 ◽  
Vol 25 (3) ◽  
pp. 619 ◽  
Author(s):  
Arthur T. Kopylov ◽  
Alexander A. Stepanov ◽  
Kristina A. Malsagova ◽  
Deepesh Soni ◽  
Nikolay E. Kushlinsky ◽  
...  

Background: Colorectal cancer (CRC) at a current clinical level is still hardly diagnosed, especially with regard to nascent tumors, which are typically asymptotic. Searching for reliable biomarkers of early diagnosis is an extremely essential task. Identification of specific post-translational modifications (PTM) may also significantly improve net benefits and tailor the process of CRC recognition. We examined depleted plasma samples obtained from 41 healthy volunteers and 28 patients with CRC at different stages to conduct comparative proteome-scaled analysis. The main goal of the study was to establish a constellation of protein markers in combination with their PTMs and semi-quantitative ratios that may support and realize the distinction of CRC until the disease has a poor clinical manifestation. Results: Proteomic analysis revealed 119 and 166 proteins for patients in stages I–II and III–IV, correspondingly. Plenty of proteins (44 proteins) reflected conditions of the immune response, lipid metabolism, and response to stress, but only a small portion of them were significant (p < 0.01) for distinguishing stages I–II of CRC. Among them, some cytokines (Clusterin (CLU), C4b-binding protein (C4BP), and CD59 glycoprotein (CD59), etc.) were the most prominent and the lectin pathway was specifically enhanced in patients with CRC. Significant alterations in Inter-alpha-trypsin inhibitor heavy chains (ITIH1, ITIH2, ITIH3, and ITIH4) levels were also observed due to their implication in tumor growth and the malignancy process. Other markers (Alpha-1-acid glycoprotein 2 (ORM2), Alpha-1B-glycoprotein (A1BG), Haptoglobin (HP), and Leucine-rich alpha-2-glycoprotein (LRG1), etc.) were found to create an ambiguous core involved in cancer development but also to exactly promote tumor progression in the early stages. Additionally, we identified post-translational modifications, which according to the literature are associated with the development of colorectal cancer, including kininogen 1 protein (T327-p), alpha-2-HS-glycoprotein (S138-p) and newly identified PTMs, i.e., vitamin D-binding protein (K75-ac and K370-ac) and plasma protease C1 inhibitor (Y294-p), which may also contribute and negatively impact on CRC progression. Conclusions: The contribution of cytokines and proteins of the extracellular matrix is the most significant factor in CRC development in the early stages. This can be concluded since tumor growth is tightly associated with chronic aseptic inflammation and concatenated malignancy related to loss of extracellular matrix stability. Due attention should be paid to Apolipoprotein E (APOE), Apolipoprotein C1 (APOC1), and Apolipoprotein B-100 (APOB) because of their impact on the malfunction of DNA repair and their capability to regulate mTOR and PI3K pathways. The contribution of the observed PTMs is still equivocal, but a significant decrease in the likelihood between modified and native proteins was not detected confidently.


1990 ◽  
Vol 220 ◽  
pp. 339-354 ◽  
Author(s):  
S. D. Heister ◽  
J. M. Mcdonough ◽  
A. R. Karagozian ◽  
D. W. Jenkins

A numerical solution for the flow field associated with a compressible pair of counter-rotating vortices is developed. The compressible, two-dimensional potential equation is solved utilizing the numerical method of Osher et al. (1985) for flow regions in which a non-zero density exists. Close to the vortex centres, vacuum ‘cores’ develop owing to the existence of a maximum achievable flow speed in a compressible flow field. A special treatment is required to represent these vacuum cores. Typical streamline patterns and core boundaries are obtained for upstream Mach numbers as high as 0.3, and the formation of weak shocks, predicted by Moore & Pullin (1987), is observed.


1973 ◽  
Vol 187 (1) ◽  
pp. 71-78 ◽  
Author(s):  
B. R. Reason ◽  
D. Dyer

We present a numerical solution for the operating conditions of a hydrodynamic porous journal bearing. The numerical method allows for the possibility of variable porosity in the bearing matrix, but the solution has been achieved on the assumption of matrix homogeneity. The relation between the various bearing parameters have been shown for a variety of bearing geometries and permeabilities enabling the operating conditions for this type of bearing to be better appreciated. A comparison of the present solution with approximate solutions used by other authors has been made, which indicates the useful working range of the approximate solutions.


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